I started really getting into anime my last year of high school so I'm still fairly new despite the tens of anime i've watched already.
I've never really cared for anything gory or mecha. I don't much like reverse-/harem either. I will tolerate it to a point, but get beyond it and I will drop the anime.
I don't know why, but I usually try to not watch what everyone and their mothers have seen. Shows like Bleach, One Piece, Inuyasha, Dragon Ball, etc.
My exceptions to this self-implemented rule are:
Yu-Gi-Oh! - because I discovered it when GX was airing on tv and I had no idea what anime was.
Death Note - because I did a search on "best anime of all time" and it came up so I watched it. Again, I knew next to nothing about anime.
Naruto (Shippuden) - because I used to watch it with my dad and I wanted to see all of it. I didn't know what anime was at this point, either.
Sword Art Online - because when I first heard of it, I thought it was some new free-to-play mmo so when I looked it up and found out it was an anime, I started watching it.
Clannad - because I was coerced by a friend to watch it. He probably would have taped me to a chair if he couldve.